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<div id="Sx1" class="ltx_section">
<h1 class="ltx_title ltx_title_section">Point-spread function (PSF)</h1>

<div id="Sx1.p1" class="ltx_para">
<p class="ltx_p">The impulse response of a microscope to a point-like source is described
by the point-spread function (PSF). Because a single molecule emitter
can be treated as an incoherent point source in SMLM data, the result
of fitting a PSF model to an image of a single molecule is an estimate
of the molecular position, its imaged size, and its intensity. ThunderSTORM
offers a choice between several PSF models and fitting procedures
based on (weighted or unweighted) least-squares methods and maximum
likelihood estimation <cite class="ltx_cite">[<a href="#bib.bib19" title="The Advanced Theory of Statistics" class="ltx_ref">1</a>, <a href="#bib.bib23" title="Optimized localization analysis for single-molecule tracking and super-resolution microscopy" class="ltx_ref">2</a>]</cite>.
</p>
</div>
<div id="Sx1.p2" class="ltx_para">
<p class="ltx_p">It has been shown <cite class="ltx_cite">[<a href="#bib.bib38" title="Precise nanometer localization analysis for individual fluorescent probes" class="ltx_ref">4</a>, <a href="#bib.bib34" title="Accuracy of the Gaussian point spread function model in 2D localization microscopy" class="ltx_ref">3</a>]</cite> that the Gaussian
function provides a very good approximation of the real PSF of a microscope.
This is mainly due to pixelation effects and the presence of noise,
which makes the difference between the Gaussian function and the real
PSF negligible. The advantage of Gaussian PSF models are their simplicity,
robustness, and computational efficiency.</p>
</div>
<div id="Sx1.SSx1" class="ltx_subsection">
<h2 class="ltx_title ltx_title_subsection">See also</h2>

<div id="Sx1.SSx1.p1" class="ltx_para">
<ul id="I1" class="ltx_itemize">
<li id="I1.i1" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i1.p1" class="ltx_para">
<p class="ltx_p"><a href="SymmetricGaussianEstimatorUI.html" title="" class="ltx_ref">Symmetric 2D Gaussian function PSF model</a></p>
</div>
</li>
<li id="I1.i2" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i2.p1" class="ltx_para">
<p class="ltx_p"><a href="IntSymmetricGaussianEstimatorUI.html" title="" class="ltx_ref">Integrated form of a symmetric 2D Gaussian function PSF model</a></p>
</div>
</li>
<li id="I1.i3" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i3.p1" class="ltx_para">
<p class="ltx_p"><a href="EllipticGaussianEstimatorUI.html" title="" class="ltx_ref">Rotated elliptical Gaussian function PSF model (3D using astigmatism)</a></p>
</div>
</li>
<li id="I1.i4" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i4.p1" class="ltx_para">
<p class="ltx_p"><a href="Fitting.html" title="" class="ltx_ref">Fitting point-spread function models</a></p>
</div>
</li>
<li id="I1.i5" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i5.p1" class="ltx_para">
<p class="ltx_p"><a href="FittingRegion.html" title="" class="ltx_ref">Definition of the fitting region</a></p>
</div>
</li>
<li id="I1.i6" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i6.p1" class="ltx_para">
<p class="ltx_p"><a href="LocalizationUncertainty.html" title="" class="ltx_ref">Localization uncertainty</a></p>
</div>
</li>
<li id="I1.i7" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i7.p1" class="ltx_para">
<p class="ltx_p"><a href="CrowdedField.html" title="" class="ltx_ref">Multiple-emitter fitting analysis</a></p>
</div>
</li>
</ul>
</div>
</div>
</div>
<div id="bib" class="ltx_bibliography">
<h1 class="ltx_title ltx_title_bibliography">References</h1>

<ul id="L1" class="ltx_biblist">
<li id="bib.bib19" class="ltx_bibitem ltx_bib_book">
<span class="ltx_bibtag ltx_bib_key ltx_role_refnum">[1]</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_author">M. Kendall and A. Stuart</span><span class="ltx_text ltx_bib_year">(1979)</span>
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_title">The Advanced Theory of Statistics</span>,
</span>
<span class="ltx_bibblock"> <span class="ltx_text ltx_bib_publisher">London: Charles Griffin</span>.
</span>
<span class="ltx_bibblock ltx_bib_cited">Cited by: <a href="#Sx1.p1" title="Point-spread function (PSF)" class="ltx_ref"><span class="ltx_text ltx_ref_title">Point-spread function (PSF)</span></a>.
</span>
</li>
<li id="bib.bib23" class="ltx_bibitem ltx_bib_article">
<span class="ltx_bibtag ltx_bib_key ltx_role_refnum">[2]</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_author">K. I. Mortensen, L. S. Churchman, J. A. Spudich and H. Flyvbjerg</span><span class="ltx_text ltx_bib_year">(2010)</span>
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_title">Optimized localization analysis for single-molecule tracking and super-resolution microscopy</span>,
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_journal">Nature Methods</span> <span class="ltx_text ltx_bib_volume">7</span> (<span class="ltx_text ltx_bib_number">5</span>), <span class="ltx_text ltx_bib_pages"> pp. 377–381</span>.
</span>
<span class="ltx_bibblock">External Links: <span class="ltx_text ltx_bib_links"><a href="http://dx.doi.org/10.1038/nmeth.1447" title="" class="ltx_ref doi ltx_bib_external">Document</a></span>.
</span>
<span class="ltx_bibblock ltx_bib_cited">Cited by: <a href="#Sx1.p1" title="Point-spread function (PSF)" class="ltx_ref"><span class="ltx_text ltx_ref_title">Point-spread function (PSF)</span></a>.
</span>
</li>
<li id="bib.bib34" class="ltx_bibitem ltx_bib_article">
<span class="ltx_bibtag ltx_bib_key ltx_role_refnum">[3]</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_author">S. Stallinga and B. Rieger</span><span class="ltx_text ltx_bib_year">(2010)</span>
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_title">Accuracy of the Gaussian point spread function model in 2D localization microscopy</span>,
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_journal">Optics Express</span> <span class="ltx_text ltx_bib_volume">18</span> (<span class="ltx_text ltx_bib_number">24</span>), <span class="ltx_text ltx_bib_pages"> pp. 24461–24476</span>.
</span>
<span class="ltx_bibblock">External Links: <span class="ltx_text ltx_bib_links"><a href="http://dx.doi.org/10.1364/OE.18.024461" title="" class="ltx_ref doi ltx_bib_external">Document</a></span>.
</span>
<span class="ltx_bibblock ltx_bib_cited">Cited by: <a href="#Sx1.p2" title="Point-spread function (PSF)" class="ltx_ref"><span class="ltx_text ltx_ref_title">Point-spread function (PSF)</span></a>.
</span>
</li>
<li id="bib.bib38" class="ltx_bibitem ltx_bib_article">
<span class="ltx_bibtag ltx_bib_key ltx_role_refnum">[4]</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_author">R. E. Thompson, D. R. Larson and W. W. Webb</span><span class="ltx_text ltx_bib_year">(2002)</span>
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_title">Precise nanometer localization analysis for individual fluorescent probes</span>,
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_journal">Biophysical Journal</span> <span class="ltx_text ltx_bib_volume">82</span> (<span class="ltx_text ltx_bib_number">5</span>), <span class="ltx_text ltx_bib_pages"> pp. 2775–83</span>.
</span>
<span class="ltx_bibblock">External Links: <span class="ltx_text ltx_bib_links"><a href="http://dx.doi.org/10.1016/S0006-3495(02)75618-X" title="" class="ltx_ref doi ltx_bib_external">Document</a></span>.
</span>
<span class="ltx_bibblock ltx_bib_cited">Cited by: <a href="#Sx1.p2" title="Point-spread function (PSF)" class="ltx_ref"><span class="ltx_text ltx_ref_title">Point-spread function (PSF)</span></a>.
</span>
</li>
</ul>
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